MIT Department of Biology
7.014 Introductory Biology, Spring 2005
Recitation Section 21 Answer Key
April 27-28, 2005
Life Tables
A. Cohort life table
You are studying the life of the common tribble. In a large tribble colony, you mark 1000 newborn
tribbles and observe them for the next 5 years. You find the following:
1. Derive formulas for and calculate the remaining values in the table, based on the following
definitions.
survivorship in year x = survival of individuals to age x
mortality rate in year x = proportion of individuals of age x dying by age x+1
age units lived in year x = mean # of individuals alive between year x and x+1
remaining life expectancy at age x = expectation of further life for individuals of age x
lx
mx
Lx
ex
5
ex =
sx =
n (x+1 )
Year
(age)
x
0
1
2
3
4
5
nx
lx =
# tribbles
alive at
start of
year
nx
1000
900
700
200
50
0
nx
n 0
m x = 1− s x
Lx =
Survivorship
Mortality
rate
lx
1
0.9
0.7
0.2
0.05
0
mx
0.1
0.22
0.71
0.75
1.00
∑L
i
i =x
nx
n x + n (x+1 )
2
Mean #
tribbles
alive in
year
Lx
950
800
450
125
25
avg. life expectancy
Average
Remaining
Life
Expectancy
ex
2.35
1.55
0.86
0.75
0.50
0.00
= x+ ex
Average life
expectancy
for
individuals of
age x
2.35
2.55
2.86
3.75
4.50
2
2. Sketch the survivorship curve for tribbles:
3. Describe this curve in words. Speculate on what could cause the qualitative shape of the curve.
1.0
Tribbles su rv iv e w ell u n til age
2, w h en su rv iv orsh ip decreases
sh arply. Perh aps at age 2, th ey
reach old age, o r beco m e old
en ou gh to be preyed u pon .
lx
0.5
0
0
1
2
3
4
5
age
4. What other types of curves are there? Describe qualitative conditions that produce these curves.
The immediate exponential decay curve applies to organisms that have a lot of offspring that die very young, such as frogs, fish, or trees. The linear decay curve applies to organisms whose probability of dying is not dependent on age. The very slow decay followed by the exponential decay curve applies to organisms that have very few offspring, and take great care to protect those offspring, such as humans. B. Replacement rates
You also collected data on the tribbles born to the cohort you are studying. This is summarized below:
YEAR
(age)
x
0
1
2
3
4
5
# tribbles alive
at start of year
nx
1000
900
700
200
50
0
# individuals born
to members of
cohort during year
x
0
1200
100
50
5
0
Fecundity
bx
0
1.33
0.14
0.25
0.10
0
lxbx
0
1.2
0.10
0.05
0.01*
0
for
question
3
0
0
2
0
0
0
for
question
4
0
0
0
4
0
0
1. Calculate the fecundity and realized fecundity (lxbx) for each age group.
i=5
2. Calculate the net reproductive rate, R 0 = ∑ l i b i . Is this population stable (R0=1), growing
i=0
(R0>1), or shrinking (R0<1)?
R0 = 1.20 + 0.10 + 0.05 + 0.01 = 1.36 therefore: growing
3. Suppose you find tribbles with the same life expectancies except that they all give birth to 2 new
tribbles only once in their lifetime, at an age of 2 years. Will the resulting population be stable?
Only one term: R0 = 1.4 therefore: growing
4. Suppose you find tribbles with the same life expectancies except that they all give birth to 4 new
tribbles only once in their lifetime, at an age of 3 years. Will the resulting population be stable?
Only one term: R0 = 0.8 therefore: shrinking. These tribbles don’t reach reproductive age until after
they’ve started to die of old age.
2